Digital signal processing may be preferred over analog signal processing in many cases, e.g. due to higher accuracy, lower power consumption, and/or smaller required circuit area. In order to process an analog signal by means of digital signal processing, it has to be converted to a digital representation. This is typically done in an analog-to-digital converter (ADC), in which the analog signal is sampled at a sample rate fs to generate a discrete-time analog signal, which is then converted to a digital representation.
Due to unwanted nonlinear behavior of e.g. the ADC and/or circuitry preceding the ADC, such as amplifiers and/or filters, the signal is normally subject to nonlinear distortion. Such nonlinear distortion may e.g. be compensated for in the digital domain using digital signal processing.
To avoid aliasing, the analog signal should be bandlimited and have a bandwidth that is less than half the sampling rate. A problem is that nonlinear distortion normally tends to increase the bandwidth of a signal. Hence, even if the (undistorted) analog signal is properly bandlimited, the nonlinearly distorted signal may well have a bandwidth that is greater than half the sampling rate. A brute-force approach to circumvent this problem is to increase the sample rate of the ADC such that the sample rate is greater than twice the bandwidth of the nonlinearly distorted signal in order to properly capture the nonlinearly distorted signal and facilitate proper compensation of the nonlinear distortion in the digital domain. However, increasing the sampling rate of the ADC is undesirable e.g. in that harder requirements, e.g. in terms of speed, is set on circuit components of the ADC, such as sample-and-hold circuits and comparators.
The article W. A. Frank et al, “Sampling requirements for Volterra system identification”, IEEE Signal Processing Letters, vol. 3, no. 9, pp. 266-268, September 1996 discloses that a sampling rate twice as high as the bandwidth of the undistorted signal suffices to correctly identify discrete Volterra kernels corresponding to continuous Volterra kernels of a nonlinear model. In the article J. Tsimbinos et al, “Input Nyquist sampling suffices to identify and compensate nonlinear systems”, IEEE Transactions on Signal Processing, vol. 46, no. 10, pp 2833-2837, October 1998, this is utilized for sampling a distorted signal at a sampling rate of twice the bandwidth of the undistorted signal and compensating for the nonlinear distortion using an inverse Volterra model. However, the use of an inverse model of Volterra type results in a relatively high computational complexity, especially for high nonlinearity orders and/or long memory, which is a disadvantage.